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Some Results on the Upper Bounds for the Adjacent Specral Radius of Graphs

Author: WangXinXia
Tutor: ShuJinLong
School: East China Normal University
Course: Operational Research and Cybernetics
Keywords: Graft Spectral radius Bicyclic Graphs Tree diagram k tree
CLC: O157.5
Type: Master's thesis
Year: 2005
Downloads: 117
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Abstract


In the map of the study , the estimate of the spectral radius of the circles has always been a hot issue . Already has a more mature theory , techniques and methods . Up to the upper bound of the spectral radius of this paper , we mainly consider general simple connected graph , tree spectral radius of bicyclic graphs community, and get some new conclusions . In addition, we also consider the special graphs k spectral radius of the tree , and specific results are as follows : 1 . Use of similarity transformation matrix to obtain a new spectrum of adjacent spectral radius of up to the upper bound : ρ (G) ≤ (Δ 2 pq ((p q-Δ 2 ) 2 4q (Δ 1 -p)) 1/2 ) / 2 Furthermore, equality holds if and only if G ≌ G 1 (?) G 2 , the G 1 i-1 -order p- regular graphs G 2 for ni 1 order ( Δ 2 < / sub > -q ) - regular graph ( unknown symbol definitions , see § 2.3) 2. research Bicyclic Graphs tree diagram T of G < / sub > structure , and thus gives the tree diagram T G spectral radius circles : ρ (T G ) ≤ (n 1-2 ((nl) 2 2l (nl 1) (n-3l 1)) 1/2 ) / 2 where l is G number of edges in two basic circle . 3 Graft characterizes the spectral radius reached Second , the third largest tree of order n k .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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